Name: SID: Discussion Session:
|
|
- Anthony Peters
- 7 years ago
- Views:
Transcription
1 Name: SID: Dscusson Sesson: Chemcal Engneerng Thermodynamcs 4 Fall 2008 Thursday, November 6, 2008 Mdterm II - 70 mnutes 00 onts Total Closed Book and Notes (20 ponts). Evaluate whether the statements are true or false. You may enter your answers on the exam sheet. a) Most compressors and turbnes have mechancal effcences of less than 0.5. FALSE. er SV&A p269: Values of η [for turbnes] usually range from 0.7 to 0.8. er SV&A p274: Compressor effcences are usually n the range of 0.7 to 0.8. b) The regeneratve cycle has a hgher effcency than the standard Rankne cycles because the latent heat that would be lost n the condenser s partally used to preheat the water enterng the boler. TRUE. Ths s a correct descrpton of the regeneratve cycle. c) The thermal effcency of a vapor compresson cycle depends on the choce of the workng flud. TRUE. The vapor compresson cycle contans an rreversble adabatc expanson; what fracton of vapor s lquefed n ths step depends on the thermodynamc propertes of the workng flud. d) In a refrgeraton cycle, the lower the evaporator temperature, the hgher the CO, retanng the rest of the cycle unchanged. FALSE. In fact, ths s exactly backward. e) For pure speces, partal molar propertes equal molar propertes. TRUE. Ths works even for entropy, because the extra -R ln x term n the entropy of a mxture drops out when x. f) At constant temperature and pressure, partal molar propertes can vary ndependently, based on Gbbs-Duhem relatonshp. FALSE. At constant T and, the Gbbs-Duhem relatonshp s x d 0 for any partal molar property M M. What ths equaton means s that partal molar propertes cannot vary ndependently, because f M changes for one speces, all the other necessarly change n a way that keeps the sum stll equal to zero. g) As pressure approaches zero, fugacty coeffcent approaches partal pressure. FALSE. Trck queston. Fugacty approaches partal pressure; fugacty coeffcent approaches. h) Fugacty of pure condensed phase at temperature T and low pressure may be approxmated by uraton pressure at temperature T. M must j
2 TRUE. Credt was gven for FALSE to those students who commented that at extremely low temperatures, the oyntng correcton can no longer be neglected, even at low pressures. Remember that all gases become deal gases n the low pressure lmt, so t s not necessary to make an added assumpton about deal gas behavor here: that assumpton s already bult n. ) Raoult s law descrbes well an deal gas n coexstence wth an deal soluton at low pressure. TRUE. Ths s exactly what Raoult s law does. j) Actvty coeffcents descrbe devatons from deal soluton behavor. TRUE. Ths s exactly what actvty coeffcents do.
3 (30 ponts) 2. Freon 34a s to be used n a refrgerator that operates wth an evaporator temperature of - 0 C and a condenser temperature of 30 C. Saturated lqud refrgerant from the condenser flows through an expanson valve nto the evaporator, from whch t emerges as urated vapor. The thermodynamc dagram for Freon 34a s gven on the next page. 4 Condenser 3 Evaporator 2 a) Draw the actual process on the enclosed -H dagram. For a refrgeraton capacty of 5000 J/s, what s the crculaton rate of the refrgerant? Readng from the -H dagram, we fnd: H H kj/kg H kj/kg Q& c m& H H 2 5kJ / s kg/s 390kJ / kg 240kJ / kg b) Suppose the cycle n part (a) s modfed by the ncluson of a countercurrent heat exchanger between the condenser and throttle valve n whch heat s transferred to vapor returnng from the evaporator. The lqud from the condenser enters the exchanger at 30 C and the vapor from the evaporator enters the exchanger at -0 C and leaves at 20 C. Draw the process on the enclosed -H dagram. What s the crculaton rate of the refrgerant?
4 4 4 Condenser 3 Evaporator 2 2 Usng an energy balance on the heat exchanger gves: H 4 + H 2 H 4 + H 2 Solvng for H 4 gves H 4 H 4 + H 2 H 2 The heat exchanger operates at constant pressure. Thus, H kj/kg. H 4 H 240 kj/kg kj/kg 420 kj/kg 20 kj/kg Q& c 5kJ / s m& kg/s ' H 2 H 390kJ / kg 20kJ / kg
5 Blue part a urple part b
6 (30 ponts) 3. a) Show that the fugacty of a vapor that obeys the volumetrc equaton of state: s gven by: V b b f V exp. The general equaton for fugacty n terms of volumetrc propertes s f exp V d 0 Our equaton of state can be rewrtten V + b Insertng ths equaton nto the general fugacty equaton gves f V exp 0 b f V exp d 0 b f V exp + b d b) Derve an equaton for the fugacty coeffcent of the lqud at uraton, functon of uraton pressure. ln φ L, as a At uraton, we have f L f V. We already know the fugacty of the vapor phase: b f V exp Evaluatng ths at the uraton pressure, we have b f f L V exp Rewrtng to solve for the fugacty coeffcent, we fnd ln φ SAT b c) When the substance used n part (a) s sothermally compressed, an ncompressble lqud s produced. Develop an equaton for the fugacty of the lqud. The equaton for the fugacty of a lqud can be wrtten
7 f L φ exp Vd And snce the lqud s ncompressble, V s not a functon of. Thus, we have f L φ exp V0 ( ) Fnally, we already know f from part (b). luggng ths n, we have b f L exp exp V0 ( ) Or V 0 V0 + b f L exp d) Now let s pass supercrtcal CO 2 over our compressed lqud. Develop an expresson for the solublty of our lqud n SCF CO 2? Assume a neglgble amount of CO 2 dssolves nto compressed lqud. The gaseous mxture obeys the followng equaton of state: V b mx wth mxng rule b y b. mx Solublty s a measure of how much of our lqud, call t speces (), wll dssolve nto the supercrtcal CO 2 phase at equlbrum. We assume the amount of CO 2 that dssolves nto the lqud phase s neglgble. Thus, the fugacty of our pure compressed lqud must be equal to the fugacty of the same substance n the CO 2 supercrtcal phase: f lqud f,supercrt Assumng the Lews-Randall rule apples n the supercrtcal phase, we have v v f φ y We have assumed that the vapor phase obeys the equaton V v To get φ, we start by applyng the defnton of partal molar fugacty: v nln φ d ln φ where ln φ ( ) n Z T, 0 We know (V-b mx ), from whch we can show ( V bmx) V bmx b mx
8 V bmx Z d bmx d bmx ln φ ( Z ) d (Note: havng done parts (a)-(c) already, you could jump rght to ths step as a startng pont.) b mx ln φ nbmx ( nb + n2b2 ) nln φ v nln φ b ln φ n T, v b ( ln ) y v f exp φ exp Now that we have the fugacty for substance n the supercrtcal phase, we equate t wth the fugacty of substance n the lqud phase, whch we already know from part (c): L v f y f V0 V0 + b exp b y exp ( V b )( ) 0 y exp Ths s essentally the equaton from lecture nvolvng the enhancement factor, only wth expressons for the fugacty coeffcents substtuted n. (20 ponts) 4. It has been dscovered that a 20 wt% soluton of acetc acd n water wll effectvely kll the majorty of common speces of weeds, whle actually encouragng the growth of desrable plants. Vnegar has the added beneft of also dscouragng ants from eatng your flowers. The molar volume of a water-acetc acd mxture at 25 C s well descrbed by the equaton V x² x , where x s the mole fracton of acetc acd n the soluton. (a) Fnd the partal molar volumes of water and acetc acd n a 20 wt% acetc acd soluton. The molecular weghts of water and acetc acd are 8.05 g/mol and g/mol, respectvely. We begn by convertng weght percent nto mole fracton: w / MW x w / MW + w / MW ( ) H2O
9 0.20 / x 0.20 / /8.05 x To fnd partal molar volumes, we use the formulas V V V + ( x ) x T, V VH 2O V ( x ) x T, Observng that V x² x , we fnd V 8.974x x T, luggng n that x gves V (8.974)(0.070) mol/ml x T, At x 0.070, V (4.4857)(0.070)² + (34.96)(0.070) mol/ml V ( 0.070)(35.589) ml/mol V (0.070)(35.589) ml/mol H O (b) After weedng your garden, you decde to make a salad, topped (of course!) wth a vnegar-and-ol dressng. What volume of 20 wt% acetc acd should be combned wth pure water to make 00 ml of a 5 wt% acetc acd soluton (eg, vnegar)? To complete ths problem, we must recognze that for non-deal solutons, volume s not addtve. If you smply add 25 ml of 20 wt% acetc acd to 75 ml of water, you wll not get a 00 ml soluton of 5 wt% acetc acd. Luckly, mass (or equvalently, number of moles) s addtve (after all, conservaton of mass s a fundamental precept of (non-relatvstc non-nuclear) physcs). We wsh to make 00 ml of 5 wt% acetc acd soluton. Agan, we begn by convertng to mole fracton: 0.05 / x 0.05 / /8.05 x To determne how many moles we actually have, we need the molar volume.
10 V *(0.055)² * ml/mol The total number of moles s thus 00 ml / ml/mol mol N 0.055* moles N H2O ( 0.055)* moles All moles of acetc acd must come from the 20 wt% (7 mol%) soluton. Thus, we need mol.929 mol of the 20 wt% (7 mol%) soluton. The molar 0.070mol molsoluton volume of that soluton was ml/mol, so we need.929 mol * ml/mol ml of 20 wt% acetc acd.
substances (among other variables as well). ( ) Thus the change in volume of a mixture can be written as
Mxtures and Solutons Partal Molar Quanttes Partal molar volume he total volume of a mxture of substances s a functon of the amounts of both V V n,n substances (among other varables as well). hus the change
More informationMean Molecular Weight
Mean Molecular Weght The thermodynamc relatons between P, ρ, and T, as well as the calculaton of stellar opacty requres knowledge of the system s mean molecular weght defned as the mass per unt mole of
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.
More informationUniversity Physics AI No. 11 Kinetic Theory
Unersty hyscs AI No. 11 Knetc heory Class Number Name I.Choose the Correct Answer 1. Whch type o deal gas wll hae the largest alue or C -C? ( D (A Monatomc (B Datomc (C olyatomc (D he alue wll be the same
More informationNumerical Analysis of the Natural Gas Combustion Products
Energy and Power Engneerng, 2012, 4, 353-357 http://dxdoorg/104236/epe201245046 Publshed Onlne September 2012 (http://wwwscrporg/journal/epe) Numercal Analyss of the Natural Gas Combuston Products Fernando
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationn + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2)
MATH 16T Exam 1 : Part I (In-Class) Solutons 1. (0 pts) A pggy bank contans 4 cons, all of whch are nckels (5 ), dmes (10 ) or quarters (5 ). The pggy bank also contans a con of each denomnaton. The total
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationSection C2: BJT Structure and Operational Modes
Secton 2: JT Structure and Operatonal Modes Recall that the semconductor dode s smply a pn juncton. Dependng on how the juncton s based, current may easly flow between the dode termnals (forward bas, v
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationInterlude: Interphase Mass Transfer
Interlude: Interphase Mass Transfer The transport of mass wthn a sngle phase depends drectly on the concentraton gradent of the transportng speces n that phase. Mass may also transport from one phase to
More informationv a 1 b 1 i, a 2 b 2 i,..., a n b n i.
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More information1 Battery Technology and Markets, Spring 2010 26 January 2010 Lecture 1: Introduction to Electrochemistry
1 Battery Technology and Markets, Sprng 2010 Lecture 1: Introducton to Electrochemstry 1. Defnton of battery 2. Energy storage devce: voltage and capacty 3. Descrpton of electrochemcal cell and standard
More informationFLASH POINT DETERMINATION OF BINARY MIXTURES OF ALCOHOLS, KETONES AND WATER. P.J. Martínez, E. Rus and J.M. Compaña
FLASH POINT DETERMINATION OF BINARY MIXTURES OF ALCOHOLS, KETONES AND WATER Abstract P.J. Martínez, E. Rus and J.M. Compaña Departamento de Ingenería Químca. Facultad de Cencas. Unversdad de Málaga. 29071
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI-30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationvap H = RT 1T 2 = 30.850 kj mol 1 100 kpa = 341 K
Thermodynamics: Examples for chapter 6. 1. The boiling point of hexane at 1 atm is 68.7 C. What is the boiling point at 1 bar? The vapor pressure of hexane at 49.6 C is 53.32 kpa. Assume that the vapor
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationFaraday's Law of Induction
Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy
More informationSeries Solutions of ODEs 2 the Frobenius method. The basic idea of the Frobenius method is to look for solutions of the form 3
Royal Holloway Unversty of London Department of Physs Seres Solutons of ODEs the Frobenus method Introduton to the Methodology The smple seres expanson method works for dfferental equatons whose solutons
More informationDerivation of Humidty and NOx Humidty Correction Factors
(Ths document follows the presentatons n "Vapor Pressure Equaton for Water n the Range 0 to 00 C", by Arnold Wexler and Lews Greenspan, February 9, 97 JOURNAL OF RESEARCH of the Natonal Bureau of Standards
More informationHedging Interest-Rate Risk with Duration
FIXED-INCOME SECURITIES Chapter 5 Hedgng Interest-Rate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cash-flows Interest rate rsk Hedgng prncples Duraton-Based Hedgng Technques Defnton of duraton
More informationWe are now ready to answer the question: What are the possible cardinalities for finite fields?
Chapter 3 Fnte felds We have seen, n the prevous chapters, some examples of fnte felds. For example, the resdue class rng Z/pZ (when p s a prme) forms a feld wth p elements whch may be dentfed wth the
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationChapter 2 Thermodynamics of Combustion
Chapter 2 Thermodynamcs of Combuston 2.1 Propertes of Mxtures The thermal propertes of a pure substance are descrbed by quanttes ncludng nternal energy, u, enthalpy, h, specfc heat, c p, etc. Combuston
More informationTopical Workshop for PhD students Adsorption and Diffusion in MOFs Institut für Nichtklassische Chemie, Germany, www.uni-leipzig.
Gas Separaton and Purfcaton Measurement of Breakthrough Curves Topcal Workshop for PhD students Adsorpton and Dffuson n MOFs Adsorpton on Surfaces / Separaton effects Useful features Thermodynamc effect
More information8 Algorithm for Binary Searching in Trees
8 Algorthm for Bnary Searchng n Trees In ths secton we present our algorthm for bnary searchng n trees. A crucal observaton employed by the algorthm s that ths problem can be effcently solved when the
More informationLiquid-Vapor Equilibria in Binary Systems 1
Lqud-Vapor Equlbra n Bnary Systems 1 Purpose The purpose of ths experment s to study a bnary lqud-vapor equlbrum of chloroform and acetone. Measurements of lqud and vapor compostons wll be made by refractometry.
More informationNMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING. Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582
NMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582 7. Root Dynamcs 7.2 Intro to Root Dynamcs We now look at the forces requred to cause moton of the root.e. dynamcs!!
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationPSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12
14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationQuotes. Research Findings. The First Law of Thermodynamics. Introduction. Introduction. Thermodynamics Lecture Series
8//005 Quotes Thermodynamcs Lecture Seres Frst Law of Thermodynamcs & Control Mass, Open Appled Scences Educaton Research Group (ASERG) Faculty of Appled Scences Unverst Teknolog MARA emal: drjjlanta@hotmal.com
More informationThe issue of June, 1925 of Industrial and Engineering Chemistry published a famous paper entitled
Revsta Cêncas & Tecnologa Reflectons on the use of the Mccabe and Thele method GOMES, João Fernando Perera Chemcal Engneerng Department, IST - Insttuto Superor Técnco, Torre Sul, Av. Rovsco Pas, 1, 1049-001
More informationBERNSTEIN POLYNOMIALS
On-Lne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More informationIntroduction to Statistical Physics (2SP)
Introducton to Statstcal Physcs (2SP) Rchard Sear March 5, 20 Contents What s the entropy (aka the uncertanty)? 2. One macroscopc state s the result of many many mcroscopc states.......... 2.2 States wth
More information) of the Cell class is created containing information about events associated with the cell. Events are added to the Cell instance
Calbraton Method Instances of the Cell class (one nstance for each FMS cell) contan ADC raw data and methods assocated wth each partcular FMS cell. The calbraton method ncludes event selecton (Class Cell
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationModern Problem Solving Techniques in Engineering with POLYMATH, Excel and MATLAB. Introduction
Modern Problem Solvng Tehnques n Engneerng wth POLYMATH, Exel and MATLAB. Introduton Engneers are fundamentally problem solvers, seekng to aheve some objetve or desgn among tehnal, soal eonom, regulatory
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More informationSection 2 Introduction to Statistical Mechanics
Secton 2 Introducton to Statstcal Mechancs 2.1 Introducng entropy 2.1.1 Boltzmann s formula A very mportant thermodynamc concept s that of entropy S. Entropy s a functon of state, lke the nternal energy.
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):1884-1889 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 610-519-4390,
More informationa) Use the following equation from the lecture notes: = ( 8.314 J K 1 mol 1) ( ) 10 L
hermodynamics: Examples for chapter 4. 1. One mole of nitrogen gas is allowed to expand from 0.5 to 10 L reversible and isothermal process at 300 K. Calculate the change in molar entropy using a the ideal
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationRisk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008
Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationThermodynamics of Mixing
Thermodynamics of Mixing Dependence of Gibbs energy on mixture composition is G = n A µ A + n B µ B and at constant T and p, systems tend towards a lower Gibbs energy The simplest example of mixing: What
More informationMOLECULAR PARTITION FUNCTIONS
MOLECULR PRTITIO FUCTIOS Introducton In the last chapter, we have been ntroduced to the three man ensembles used n statstcal mechancs and some examples of calculatons of partton functons were also gven.
More informationHÜCKEL MOLECULAR ORBITAL THEORY
1 HÜCKEL MOLECULAR ORBITAL THEORY In general, the vast maorty polyatomc molecules can be thought of as consstng of a collecton of two electron bonds between pars of atoms. So the qualtatve pcture of σ
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationLecture 2 The First Law of Thermodynamics (Ch.1)
Lecture he Frst Law o hermodynamcs (Ch.) Outlne:. Internal Energy, Work, Heatng. Energy Conservaton the Frst Law 3. Quas-statc processes 4. Enthalpy 5. Heat Capacty Internal Energy he nternal energy o
More information5.74 Introductory Quantum Mechanics II
MIT OpenCourseWare http://ocw.mt.edu 5.74 Introductory Quantum Mechancs II Sprng 9 For nformaton about ctng these materals or our Terms of Use, vst: http://ocw.mt.edu/terms. 4-1 4.1. INTERACTION OF LIGHT
More informationIS-LM Model 1 C' dy = di
- odel Solow Assumptons - demand rrelevant n long run; assumes economy s operatng at potental GDP; concerned wth growth - Assumptons - supply s rrelevant n short run; assumes economy s operatng below potental
More informationTHERMAL PROPERTIES OF MATTER 12
HERMAL PROPERIES OF MAER Q.. Reason: he mass o a mole o a substance n grams equals the atomc or molecular mass o the substance. Snce neon has an atomc mass o 0, a mole o neon has a mass o 0 g. Snce N has
More informationChapter 11 CLOUD DYNAMICS AND CHEMISTRY
Chapter 11 CLOUD DYNAMICS AND CHEMISTRY Shawn J. Roselle * and Francs S. Bnkowsk ** Atmospherc Modelng Dvson Natonal Exposure Research Laboratory U.S. Envronmental Protecton Agency Research Trangle Park,
More informationShielding Equations and Buildup Factors Explained
Sheldng Equatons and uldup Factors Explaned Gamma Exposure Fluence Rate Equatons For an explanaton of the fluence rate equatons used n the unshelded and shelded calculatons, vst ths US Health Physcs Socety
More informationInter-Ing 2007. INTERDISCIPLINARITY IN ENGINEERING SCIENTIFIC INTERNATIONAL CONFERENCE, TG. MUREŞ ROMÂNIA, 15-16 November 2007.
Inter-Ing 2007 INTERDISCIPLINARITY IN ENGINEERING SCIENTIFIC INTERNATIONAL CONFERENCE, TG. MUREŞ ROMÂNIA, 15-16 November 2007. UNCERTAINTY REGION SIMULATION FOR A SERIAL ROBOT STRUCTURE MARIUS SEBASTIAN
More informationEXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A CALCULATOR
EXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A CALCULATOR 8S CHAPTER 8 EXAMPLES EXAMPLE 8.4A THE INVESTMENT NEEDED TO REACH A PARTICULAR FUTURE VALUE What amount must you nvest now at 4% compoune monthly
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationTrade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity
Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton
More informationPotential Explosion Hazards due to Evaporating Ethanol In Whisky Distilleries HSL/2003/08
Harpur Hll, Buxton, SK17 9JN Telephone: +44 (0)114 289 2000 Facsmle: +44 (0)114 289 2050 Potental Exploson Hazards due to Evaporatng Ethanol In Whsky Dstlleres HSL/2003/08 Crown copyrght 2003 Project Leader:
More informationThe Development of Web Log Mining Based on Improve-K-Means Clustering Analysis
The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationAP Physics B 2009 Free-Response Questions
AP Physcs B 009 Free-Response Questons The College Board The College Board s a not-for-proft membershp assocaton whose msson s to connect students to college success and opportunty. Founded n 1900, the
More informationEnergies of Network Nastsemble
Supplementary materal: Assessng the relevance of node features for network structure Gnestra Bancon, 1 Paolo Pn,, 3 and Matteo Marsl 1 1 The Abdus Salam Internatonal Center for Theoretcal Physcs, Strada
More information4 Cosmological Perturbation Theory
4 Cosmologcal Perturbaton Theory So far, we have treated the unverse as perfectly homogeneous. To understand the formaton and evoluton of large-scale structures, we have to ntroduce nhomogenetes. As long
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationQuasi-Hyperbolic Discounting and Social Security Systems
Quas-Hyperbolc Dscountng and Socal Securty Systems Mordecha E. Schwarz a and Eytan Sheshnsk b May 22, 26 Abstract Hyperbolc countng has become a common assumpton for modelng bounded ratonalty wth respect
More informationChapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT
Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the
More informationA Probabilistic Theory of Coherence
A Probablstc Theory of Coherence BRANDEN FITELSON. The Coherence Measure C Let E be a set of n propostons E,..., E n. We seek a probablstc measure C(E) of the degree of coherence of E. Intutvely, we want
More informationSpecification of Selected Performance Monitoring and Commissioning Verification Algorithms for CHP Systems
PNNL-16068 Specfcaton of Selected Performance Montorng and Commssonng Verfcaton Algorthms for CHP Systems MR Brambley S Katpamula October 2006 Prepared for the U.S. Department of Energy under Contract
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationProduct-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks
Bulletn of Mathematcal Bology (21 DOI 1.17/s11538-1-9517-4 ORIGINAL ARTICLE Product-Form Statonary Dstrbutons for Defcency Zero Chemcal Reacton Networks Davd F. Anderson, Gheorghe Cracun, Thomas G. Kurtz
More informationDEGREES OF EQUIVALENCE IN A KEY COMPARISON 1 Thang H. L., Nguyen D. D. Vietnam Metrology Institute, Address: 8 Hoang Quoc Viet, Hanoi, Vietnam
DEGREES OF EQUIVALECE I A EY COMPARISO Thang H. L., guyen D. D. Vetnam Metrology Insttute, Aress: 8 Hoang Quoc Vet, Hano, Vetnam Abstract: In an nterlaboratory key comparson, a ata analyss proceure for
More informationHow To Solve A Problem In A Powerline (Powerline) With A Powerbook (Powerbook)
MIT 8.996: Topc n TCS: Internet Research Problems Sprng 2002 Lecture 7 March 20, 2002 Lecturer: Bran Dean Global Load Balancng Scrbe: John Kogel, Ben Leong In today s lecture, we dscuss global load balancng
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationtotal A A reag total A A r eag
hapter 5 Standardzng nalytcal Methods hapter Overvew 5 nalytcal Standards 5B albratng the Sgnal (S total ) 5 Determnng the Senstvty (k ) 5D Lnear Regresson and albraton urves 5E ompensatng for the Reagent
More informationMolar Mass of Butane
Cautions Butane is toxic and flammable. No OPEN Flames should be used in this experiment. Purpose The purpose of this experiment is to determine the molar mass of butane using Dalton s Law of Partial Pressures
More informationChapter 18 Homework Answers
Chapter 18 Homework Answers 18.22. 18.24. 18.26. a. Since G RT lnk, as long as the temperature remains constant, the value of G also remains constant. b. In this case, G G + RT lnq. Since the reaction
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6 - The Time Value of Money. The Time Value of Money
Ch. 6 - The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21- Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More information5 Solving systems of non-linear equations
umercal Methods n Chemcal Engneerng 5 Solvng systems o non-lnear equatons 5 Solvng systems o non-lnear equatons... 5. Overvew... 5. assng unctons... 5. D ewtons Method somethng you dd at school... 5. ewton's
More informationModelling of Hot Water Flooding
Unversty of Readng Modellng of Hot Water Floodng as an Enhanced Ol Recovery Method by Zenab Zargar August 013 Department of Mathematcs Submtted to the Department of Mathematcs, Unversty of Readng, n Partal
More informationJet Engine. Figure 1 Jet engine
Jet Engne Prof. Dr. Mustafa Cavcar Anadolu Unversty, School of Cvl Avaton Esksehr, urkey GROSS HRUS INAKE MOMENUM DRAG NE HRUS Fgure 1 Jet engne he thrust for a turboet engne can be derved from Newton
More informationThe Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1
EWEA, Specal Topc Conference 24: The Scence of Makng Torque from the Wnd, Delft, Aprl 9-2, 24, pp. 546-555. The Effect of Mean Stress on Damage Predctons for Spectral Loadng of Fberglass Composte Coupons
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationCHAPTER 8 Potential Energy and Conservation of Energy
CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and non-conservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated
More informationAddendum to: Importing Skill-Biased Technology
Addendum to: Importng Skll-Based Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationImplementation of Deutsch's Algorithm Using Mathcad
Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages - n "Machnes, Logc and Quantum Physcs"
More informationThe Full-Wave Rectifier
9/3/2005 The Full Wae ectfer.doc /0 The Full-Wae ectfer Consder the followng juncton dode crcut: s (t) Power Lne s (t) 2 Note that we are usng a transformer n ths crcut. The job of ths transformer s to
More information